Begging the question as I understand it is when you assume the conclusion is true in your premise.
If begging the question is invalid, but the reason begging the question is invalid begs the question, then begging the question must be valid, leading to a contradiction.
Therefore, to show that begging the question is invalid you can’t beg the question so why is begging the question invalid without begging the question?
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Let’s take a practical example, the equation “x + 2 = 7”, and we search for the value of “x”.
Let’s look at three different “proofs”:
1. “x + 2 = 7” is equivalent to “x +2 -2 = 7 -2” so “x = 5”, and that’s our solution => This proof is correct!
2. If we assume that 42 is the answer to this question then that means that “x = 42”, so that’s our solution => This proof is false. It makes an assumption from nowhere to force the result to be equal to 42, even if that doesn’t match at all the initial equation. This is why begging the question is invalid.
3. If we assume that 5 is the answer to this question then that means that “x = 5”, so that’s our solution => This proof is still false. It doesn’t matter than the end result is correct, that proof is still invalid.
And that third proof is much more alike what you will find in actual conversations: the problem is not necessarily that what the peoples are saying is false, the problem is that their argument makes no sense because it use some “begging the question” which as showed in the second proof doesn’t guaranty that the result is true. The point of a proof is to **100% guaranty** that the result is correct. As soon as you use the “begging the question” fallacy, then it breaks the guaranty. The result might still be true, but the argument is still invalid.
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